Animate a spheres system as a camera diaphragm
If you don't need the circles to morph so they never intersect, you can quickly fake it using a few dupligroup instances.

Create a singe circle, use an array modifier over it with the option Object Offset and Relative offset. Exactly over it add an empty object and scale it down as desired (in my example by a factor of $0.8$).



Create a group from the arrayed circle, and add a instance of it in a separate scene. Place the 3D Cursor at the desired position for the center of the iris, press . (Period Key) to use it as pivot for transforms, then duplicate-rotate the circle instance around it several times to fill a circle with the desired number of times.

Animate them by keyframing the rotation property, rotating around individual centers with Ctrl + .



Have in mind that this technique will cause intersections at more extreme angles. If you wish to compensate for those you will probably also have to animate the scale property of either the circles or the array empty. You may also look into Animation Nodes addon for a node based procedural setup.